_gr_ore_poly_divrem, gr_ore_poly_divrem, gr_ore_poly_div, gr_ore_poly_rem

Compute the right Euclidean division U = QV + R with \operatorname{ord} R < \operatorname{ord} V, which exists and is unique when the leading coefficient of V and its images under the powers of \sigma are invertible (over a field with \sigma injective, for instance). Each step divides the leading coefficient of the current remainder by \sigma^k(\operatorname{lc}(V)) and subtracts c D^k V, for k from \operatorname{ord} U - \operatorname{ord} V down to 0; the eliminated coefficients of R are then set to exact zeros (in inexact rings they would otherwise only be approximately zero). The non-underscore functions return GR_DOMAIN if V = 0; the underscore version requires \mathit{lenU} \ge \mathit{lenV} \ge 1 and writes \mathit{lenU} - \mathit{lenV} + 1 coefficients of Q and \mathit{lenU} of R. (In FLINT 3.6 and earlier the last step, k = 0, was skipped, so that for example D^2 + D + 1 divided by D gave Q = D and R = 1 + D.)